# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a361337 Showing 1-1 of 1 %I A361337 #36 Apr 16 2023 21:36:44 %S A361337 0,10,20,25,30,40,45,50,52,54,55,56,58,59,60,65,69,70,78,80,85,87,90, %T A361337 95,96,100,101,102,103,104,105,106,107,108,109,110,115,120,125,128, %U A361337 129,130,134,135,136,138,140,144,145,150,152,153,154,155,156,157,158,159 %N A361337 Numbers that reach 0 after a suitable series of split-and-multiply operations (see Comments for precise definition). %C A361337 We always split the integer N into two integers, then multiply them (and iterate). For example, 2023 can be split into 20 and 23 (producing 20*23 = 460), or split into 202 and 3 (producing 202*3 = 606). The split 2 and 023 is forbidden, as 023 is not an integer (but 460 can be split into 46 and 0 as 0 is an integer). %C A361337 The sequence lists numbers which reach 0 after a suitable sequence of splits and multiplications. %C A361337 If we multiply ALL the digits at each step, we get A034048 (115 is the first term where they differ). %C A361337 The complement (A361978) appears to be finite, containing only 219 members, the largest being 3111. - _Michael S. Branicky_, Apr 02 2023 %C A361337 More precisely, {811, 911, 913, 921, 1111, 1112, 1113, 1121, 1122, 1131, 1211, 1231, 1261, 1311, 1321, 1612, 2111, 2121, 2211, 3111} are the only numbers not in the sequence, between 792 and at least 10^7. - _M. F. Hasler_, Apr 05 2023 %H A361337 Michael S. Branicky, Table of n, a(n) for n = 1..10000 %F A361337 a(2894 + k) = 3112 + k for all k >= 0 (conjectured). - _M. F. Hasler_, Apr 05 2023 %e A361337 We see that 115 reaches 0 when split into 11*5: 11*5 = 55 -> 5*5 = 25 -> 2*5 = 10 -> 1*0 = 0. %o A361337 (Python) %o A361337 def ok(n): %o A361337 if n < 10: return n == 0 %o A361337 s = str(n) %o A361337 if "0" in s: return True %o A361337 return any(ok(int(s[:i])*int(s[i:])) for i in range(1, len(s))) %o A361337 print([k for k in range(116) if ok(k)]) # _Michael S. Branicky_, Apr 02 2023 %o A361337 (Python) ok = lambda n: '0' in (s:=str(n)) or any(ok(int(s[:i])*int(s[i:])) for i in range(1,len(s))) # _M. F. Hasler_, Apr 05 2023 %o A361337 (PARI) select( {is_A361337(n)=!vecmin(digits(n))|| for(p=1,logint(n,10), is_A361337(vecprod(divrem(n,10^p)))&& return(1))}, [1..160]) \\ _M. F. Hasler_, Apr 05 2023 %Y A361337 Cf. A031346, A034048, A361978. %Y A361337 Supersequence of A011540. %K A361337 nonn,base %O A361337 1,2 %A A361337 _N. J. A. Sloane_, Apr 01 2023, based on a posting to the Sequence Fans mailing list by _Eric Angelini_, Mar 20 2023 %E A361337 a(38) and beyond from _Michael S. Branicky_, Apr 02 2023 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE